STAT 523: Advanced Theory of Probability

Spring Quarter 1999

Tentative Syllabus (last updated: 3/29/99)

Course personnel:

• Professor: Jon A. Wellner
• B320 Padelford Hall
• Phone: 543-6207
• Office hours: 1:30 - 3:30 MWF; or by appointment

Administrative Information:

• Time(s): MWF 11:30 - 12:20
  
• Place: Bagley 331A

Prerequisites:

• Math/Stat 522 for 523.
• An interest in probability theory.

Required Texts:

• Williams, D, Probability with Martingales.
• Probability for Statisticians, by G. R. Shorack, 1998 (will be handed out as the course progresses). Foundations of Modern Probability, by Olav Kallenberg, 1998. Required.

Supplemental texts:

• Billingsley, P., (1986). Probability and Measure.
• Breiman, L., (1968). Probability.
• Chow, Y.S., and Teicher, H. (1978). Probability Theory.
• Chung, K. L., (1974). A Course in Probability Theory.
• Feller, W. (1957). An Introduction to Probability Theory and Its Applications, Volume I.
• Feller, W. (1966). An Introduction to Probability Theory and Its Applications, Volume II.
• \item Lo\'eve, M., Probability Theory, I and II.

Grading:

• Homework: 33%
• Final: 33%
  (Scheduled time & date: 2:30 - 4:20 PM, Wednesday, June 9.
• Project: 34%

Lectures:

The lectures in 523 will cover Shorack's Chapters 13-15, followed by chapter 12, and then more on Brownian motion and stochastic calculus from Kallenberg.

• Chapter 13: Characteristic functions.
• Chapter 14: CLT's via characteristic functions.
• Chapter 15: Infinitely divisible and stable distributions.
• Chapter 12: Brownian motion, embedding, and empirical processes
• Selections from Kallenberg's Chapters 15-16 and 19-21.

Click here to return to Jon Wellner's home page.

Click here to return to the Statistics Dept. home page.

Click here to return to the University of Washington home page.